Problem: Factor completely. $25d^8-80d^4+64=$
$\begin{aligned} &\phantom{=}25 d ^8 - 80 d ^4 + 64 \\\\ &= ({5 d ^4})^2 - 2({5 d ^4})({8 })+({8 })^2 \end{aligned}$ Using the square of a difference pattern: $\begin{aligned} &\phantom{=}({5 d ^4})^2 - 2({5 d ^4})({8 })+({8 })^2 \\\\ &=({5 d ^4} - {8 })^2 \end{aligned}$ In conclusion, $25 d ^8 - 80 d ^4 + 64 =(5 d ^4 - 8 )^2$ Remember that you can always check your factorization by expanding it.